Worksheet on Compound Interest when Interest is Compounded Half-Yearly

Practice the questions given in the worksheet on compound interest when interest is compounded half-yearly.

When the interest is compounded half-yearly (two times is a year) the,

A = P(1 + \(\frac{r}{2 × 100}\))\(^{n × 2}\)

i.e., the rate percent is divided by 2 and the number of years is multiplied by 2.

1. Find the compound interest and the amount on $ 4,000 at 4% per annum for 1 year when interest is compounded half-yearly.

2. Calculate the amount when sum of $ 4,800 is invested at 8% per annum for 4 years, the compound interest being compounded half-yearly.

Do not use mathematical tables. Use the necessary information from the following:

(1.08)\(^{4}\) = 1.3605; (1.04)\(^{8}\) = 1.3686

(1.08)\(^{8}\) = 1.8509; (1.04)\(^{4}\) = 1.1699

3. Calculate the compound interest at 8% per annum, compounded half-yearly, on $ 3,000 for 1\(\frac{1}{2}\) years.

4. Find the difference between the compound interest compounded yearly and half-yearly on $ 10,000 for 18 months at 10% per annum.

5. Find the compound interest and the amount on $ 5,000 at the annual interest rate of 8% for 2 years 6 months.

6. A man invests 4 10,000 in a bank for 1 ½ years at the interest rate of 7\(\frac{1}{2}\)% per annum, compounded annually. Find the amount he will receive at the end of the period.

7. Calculate the compound interest on $ 60,000 for 1 year, at 8% per annum, compounded half-yearly.

8. In what time will a sum of $ 8,000 become $ 9,261 at the interest rate of 10% per annum if the interest is compounded six-monthly?

9. At 4% per annum, find the compound interest on a certain sum of money for 1 year, compounded six-monthly, when the simple interest on this sum of money for 2 years at the rate of interest 4% per annum is $ 450.

10. Calculate the compound interest on $ 3500 at 6% per annum for 3 years, the interest being compounded half-yearly.

Do not use mathematical tables. Use the necessary information from the following:

(1.06)\(^{3}\) = 1.191016; (1.03)\(^{3}\) = 1.092727

(1.06)\(^{6}\) = 1.418519; (1.03)\(^{6}\) = 1.194052

Answers for the worksheet on compound interest when interest is compounded half-yearly are given below.

Answers:

1. $ 161.60, $ 4161.60

2. $ 6,569.28

3. $ 374.60

4.$ 26.25

5. $ 1,065.28, $ 6,065.28

6. $ 11,153.13

7. $ 4896

8. 1\(\frac{1}{2}\) years.

9. $ 227.25

10. $ 679.18

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